Periodicity is a frequently happening phenomenon for moving objects. Finding periodic behaviors is essential to understanding object movements. However, periodic behaviors could be complicated, involving multiple interleaving periods, partial time span, and spatiotemporal noises and outliers. In this paper, we address the problem of mining periodic behaviors for moving objects. It involves two sub-problems: how to detect the periods in complex movement, and how to mine periodic movement behaviors. Our main assumption is that the observed movement is generated from multiple interleaved periodic behaviors associated with certain reference locations. Based on this assumption, we propose a two-stage algorithm, Periodica, to solve the problem. At the first stage, the notion of reference spot is proposed to capture the reference locations. Through reference spots, multiple periods in the movement can be retrieved using a method that combines Fourier transform and autocorrelation. At the second stage, a probabilistic model is proposed to characterize the periodic behaviors. For a specific period, periodic behaviors are statistically generalized from partial movement sequences through hierarchical clustering. Empirical studies on both synthetic and real data sets demonstrate the effectiveness of our method.